Fullerene graphs
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In graph theory, a fullerene graph is a cubic 3-connected planar graph with exactly 12 pentagonal faces and an optional number of hexagonal faces. Fullerene graphs are the Schlegel representations of the corresponding fullerene compounds.
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| 20-fullerene (dodecahedral graph) | 24-fullerene | 26-fullerene |
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| 60-fullerene (truncated icosahedral graph) | 70-fullerene |
(If you only count 11 pentagons, remember that the perimeter counts as one.)